((y-8)^2)/4-((x-5)^2)/9 =1

解答

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

(h, k) = (5, 8), a = 2, b = 3

求解步骤

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

将

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

改写为标准双曲线方程形式

\frac{( y - 8 ) ^{2}}{2 ^{2}} - \frac{( x - 5 ) ^{2}}{3 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (5, 8), a = 2, b = 3

4 x^{2} - y^{2} - 4 y - 40 = 0

x^{2} - y^{2} + 4 x - 6 y = 6

x^{2} - 4 y^{2} - 8 x + 16 y - 36 = 0

2 = x^{2} - y^{2}

- 5 x^{2} + 4 y^{2} = 16